13 Two monochromatic waves, each of amplitude a, have
random phase difference between them. When these
superpose, then the amplitude of resultant wave is given by:
(a) root 2a
(b) 2a
(c) 4a
(d) zero
Answers
Answer:
Option (a)
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It's too simple dear....
I is directly proportional to A^2.....
Since nothing is given in question we assume the source to be coherent....
Then Intensity of both the waves = I = Io = Io....
So....
After superposition by vector method of superposition given in SHM in HC VERMA...
(A net )^2= (A1)^2+ (A2)^2 + 2(A1A2)cosX....
But in your question actually phase difference is random....
That is in above formula cosX is not constant as X is the phase difference here...
So if it is varying continously then in such case we can't find either maxima of intensity or minima of intensity....
For example in your room when you study under the bulb you do not see minima or maxima but you see average of all the possible intensity....
This is because Intensity keeps changing between maximum to minimum with a very high frequency of 10^14 times per second....
In your room at a particular point you see an average of intensity varying from maximum to minimum... So in 1 second your eyes can not differentiate between varying intensities (10^14 /second)....
Reason behind this is the bulb in your room is coherent but since bulb glows because gas filled in the bulb have infinite number of atoms... Different atom have electrons in different excited states by taking energy from electricity.....
So when the excited electrons comes to the ground state or any other lower state it emits energy in form of different electromagnetic waves..... Since electrons in different atoms are in different excited state... Electromagnetic waves coming from them have different phase difference similar to your question's situation....
In these case we take average intensity.... Not 0 for minima... Not 4 Io for maxima....
Average of cosX is 0 (But how?.... Actually it have a mathematical proof... Not required for medical students.... IITIANs you know)
So keep in the formula...
(A net )^2= (A1)^2+ (A2)^2 + 2(A1A2)cosX....
So,
(A net )^2= (A1)^2+ (A2)^2
Here since source is coherent.... A1 = A2 = A....
So ,
(A net )^2= (A)^2+ (A)^2
(A net )^2= 2(A)^2
And therefore...
A net ( or resultant amplitude) = (2)^1/2 *A
Option (a) is therefore correct...
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On brainly you will not find anyone who have good knowledge...
They just copy answer from GOOGLE..... Like the above answer who said option (a) is correct...
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